I thought it might be interesting to forum members if I gave a series of short posts on topics related to the calendar. If you are interested, please read the introduction to the series here http://forums.samurai-archives.com/viewtopic.php?p=56689.
My first topic is the cycles, the 干支 (eto or kanshi).

Most people know that years in China (and Japan) are given animal names. Many may even know that this is the Year of the Tiger. But these animal names are not an isolated phenomenon.

In China three cycles of characters have been used for various puroposes. One is the 12-cycle (stems) that starts off 子、丑、寅、卯、the characters translated as rat, ox, tiger, rabbit, etc., Another cycle is a 10-cycle that starts off 甲、乙、丙 and is usually translated as "elder brother of wood," "younger brother of wood," "elder brother of fire, " etc. The third, the 60-cycle (sexegenary cycle) combines the two, so we have 甲子、丙寅、辛亥, etc.

Q1. Without looking anything up, give examples that you have read about or come across of what any of these cycles are used for. For example, as mentioned above, the 12-cycle can be used for naming years.

For the questions below, use any resources you have.
Q2. About when do we have the first indisputed actual examples of the use of cycle(s)?
A. 13th cent. BC
B. 8th cent. BC
B. 2nd cent BC
C. 5th cent. AD

Q1. Without looking anything up, give examples that you have read about or come across of what any of these cycles are used for. For example, as mentioned above, the 12-cycle can be used for naming years.

The cycle can be used for days and hours as well as years. For hours, it is the strict 12-cycle system, each "animal" being one 2-hour frame of time, with the middle of "NE" and "UMA" being at 12 midnight and 12 noon, respectively (hence "午前" and "午後" for AM and PM (before or after the hour of the horse).

When used for days, the 12 stems are paired up with the 10 branches, as with years, and thus you get 60 cycles of days. In Japan, each month was only 30 days, although in China the months changed as dictated by the court astronomers via their calculations of various heavenly phenomena; I don't know whether the Chinese always let the stem-branch system finish, however.

I am not sure if it was used for months. It only makes sense that it was, since that is a very natural "12", but I can't think of any examples right off the top of my head. Rather, months were more popularly referred to either by their number or by various poetic descriptions.

Bethetsu wrote:

For the questions below, use any resources you have.
Q2. About when do we have the first indisputed actual examples of the use of cycle(s)?
A. 13th cent. BC
B. 8th cent. BC
C. 2nd cent BC
D. 5th cent. AD

I'm curious as to whether you mean in Japan or in China. Your BC dates make me think the latter.

The problem with (A) is that "indisputed". Oracle bones would be the primary marker I could think of, and the characters exist--but do they represent the actual cycle, yet? I guess I could dispute it just to make my reasoning correct.

I would go with 8th Century BC, since it was used in the Spring and Autumn Annals of the State of Lu. My problem here is that it could have been "retconned" into history at a later date, but since it would still be before any of they other dates listed, that would be my guess.

Though you could, I guess, dispute the provenance of Spring and Autumn Annals of the State of Lu.

Bethetsu wrote:

Q3 Which cycle (or cycles) is it?

It appears to use the sexagenarian cycle, but I can't find anything I trust sufficiently to corroborate that.

Bethetsu wrote:

Q3 What was it used for?

For days, apparently.

Bethetsu wrote:

Q4 Which of the three cycles was probably the first to develop?

I would guess that the 12-cycle was likely the first, as it seems that many cultures realized that there are 12 "moons" in one solar year, usually. The 10 branches I wonder about--10 is an easy number, but I don't see a direct correlation in any temporal quality. I suspect the system of 10 was to help work out the daily cycles, and the equation with the five elements was a part of the Han synthesis, but I'm not sure on that one.

That's what I get for answering from the Taipei airport, I guess I'm looking forward to the actual answers.

It doesn't quite count as a "cycle" as it doesn't change over time, or measure time, but the same arrangement of symbols is used for space as well, that is, for naming direction and location.

This is how we end up with, for example, the northwest tower in a castle being called the inui yagura, 'inu' and 'i' being, respectively, the same Dog and Pig/Boar as in "Year of the Dog" and "Year of the Boar."

Arrange all the symbols on a wheel like is used for the clock, and you can use it for direction as well._________________My blog on Japanese art & history: http://chaari.wordpress.com

Q1. Without looking anything up, give examples that you have read about or come across of what any of these cycles are used for. For example, as mentioned above, the 12-cycle can be used for naming years.

Well, the twelve year cycle also lent its names to the hours of the day in Japan. Ayame tells me the concepts of the 60 year cycles were/are very important in Japanese fortune telling and onmyoji, one of her favorite subjects. As I also recall it was sometimes customary to change 'era names' in Japan upon reaching certain years in the 60 year cycle (part of the onmyoji influence).

Bethetsu wrote:

Q2. About when do we have the first indisputed actual examples of the use of cycle(s)?
A. 13th cent. BC
B. 8th cent. BC
B. 2nd cent BC
C. 5th cent. AD

Assuming we're talking about overall and not just Japan, from the one source I have at hand it looks like A) 13th cent BC

although 'indisputed/undisputed' could easily change that

Bethetsu wrote:

Q3 Which cycle (or cycles) is it?

the ten celestial stems

Bethetsu wrote:

Q3 What was it used for?

dates/days of the week

Bethetsu wrote:

Q4 Which of the three cycles was probably the first to develop?

the earthly branches (12 year cycle) are thought to be older than the stems

Thank you for your answers. Days, years, time, and direction cover the major cycles, though I will add for Japan that at least the first four elements of the 10-cycle were also sometimes used to designate the night hours from inu to tora. In modern Japan the use of the 10-cycle is mainly limited to indicating rankings, as for academic grades, or for distinguishing parties in a contract (such as, "Kô甲 agrees to pay to otsu乙 or an agent that otsu selects...").

Tatsu is certainly right that the kanshi system was basic to calendar divination, I think starting from around the Han period, to the present.

Here are two other uses.
One of the first uses of the 12-cycle was marking the position of Jupiter in the sky (3rd centry BC?). It takes about 12 years for Jupiter to circle the sun, so at one point a year was named by the position of Jupiter along the elipse. However, this was not exact, and eventually years were named by the 60-cycle in order, ignoring the position of Jupiter.

Below I will use 3-10 to mean the third element of the stem cycle, 8-12 to mean the 8th elecment of the branch cycle, and (10, 8 ), (10,8 ;20) or 20-60 for the 60-cycle.

The 12-cycle aparently started being used for months in about the same time, 3rd cent. BC, though in a limited way. Month 1-12 子 is the month that contains the winter solstice, 4-12 卯the one that contains the spring equinox, etc. But I have seen them used only in two contexts. One is historical, saying which month is the first month of the year. In late Chou the first month was 1-12 建子 (おざす ね;建 refers to the orientation of the Great Dipper. ）. Since the Han period it has almost always been 3-10 建寅, which means that the month with the winter solstice 建子 is the 11th month. The cycle is also used to name months for calendar divination-- it is prefixed by a 10-cycle character. So in 1857 the first month of the year was the month 建壬寅 (9, 3); and the first month of the next year was 建甲寅 (1、3). (Intercalary months have the same cyclic number as the previous month) But these are not used for ordinary dating.

Quote:

In Japan, each month was only 30 days, although in China the months changed as dictated by the court astronomers via their calculations of various heavenly phenomena; I don't know whether the Chinese always let the stem-branch system finish, however.

This is why I think my class is necesary. Thank you for bringing them up.
I will discuss these more later but for now I will say this.

"In Japan, each month was only 30 days": apparently this is an internet legend (where did you get it?), though I have seen it on a website that should have known better. The slightest investigation will show it false. Try looking at a table of corresponding Japanese-Western dates. or a website that corrolates the two. Or take two events at least 5 months apart that you have both Japanese and Western dates for, and see if you can fit all-30-day months into the difference in days between them.

"Although in China the months changed as dictated by the court astronomers via their calculations of various heavenly phenomena...": What is said about China is true, but the "although" is wrong. The Japanese used Chinese calendar procedures, though usually not the current calendar procedures, at least from the beginning of the 7th century AD. This was true until 1685, after which the Japanese used modified Chinese calendar procedures. The 1685 and 1798 modifications used a knowledge of Western science.

"I don't know whether the Chinese always let the stem-branch system finish, however": The cycle did not skip for anything. 1 was always preceded by 60. So any given cyclic day could occur on any month-day of any month. To pick a random day, there was bound to be a 5th month, 18th day, 43-60 day in some year.

This is discussion of questions 2-4.

The earliest examples of the cycles, indeed, the earliest examples of Chinese writing, come from the Shang-period oracle bones that were discovered about a century ago, along with some bronze items with closely-related inscriptions. The earlier items problably date from the middle of the 13th century BC.

The 60-cycle was clearly fully developed and used in the oracle bones, though there are cases where the 10-cycle is used by itself, though usually part of a oracle dated by the 60-cycle. Use of the 12-cycle by itself is extremely rare.

The 60-cycle was used for naming days, and it still is. Usually the date in the 60-cycle of asking the oracle was given at the beginning of the oracle.

The 10-cycle probably developed first. One can best think about it as the names of the days of a ten-day week. Neither the names nor the characters seemed to be derived from characters of other meanings. The 12-cycle may have developed to extend the 10-cycle. There are tables where the 60-cycle is listed in columns of 10, so all the rows have the same 10-cycle name. There does not seem to be evidence that the 12-cycle was developed separately and then combined with the 10-cycle. Tatsu, you said the 12 developed first. What use and period does your source give for it?

There is no reason not to think that the 60-cycle has not continued without a break from Shang period down to the present day, but that cannot be proved. There have been some attempts to link dates with supposed eclipse records, but there are only a few records, and such attempts assume the continuation of the cycle. Furthermore, hardly any inscriptions have months or years.
However, some 500 years later, the Spring and Autumn Annals of the State of Lu (covering 722-481 BC) that JLBadgley mentioned, are different. The Annals are considered to be reasonably good history, and there is no question about the year of their events. They give most of the dates in the form month + 60-cycle day, as 五月丙午. There are 37 eclipses in the Annals, 31 of which can be firmly identified by modern methods. Since there are so many with firm years and ordering, it is clear that at least from that time to the present, the cycle of days has been unbroken.

Going back to the Shang period, the names of the rulers from that period were known from the great Han-period historical work of Shiba Sen司馬遷, the Shiki 史記 (91BC). They had names that contained the 10-cycle, as
上甲 報乙 報丙 報丁 示壬 示癸 大乙 大丁 大甲 外丙.
Now that we have the oracles, it is clear that these were posthumous names used in the family cult that gave the day of the 10-day week on which sacrifices were normally made to them according to an elaborate schedule.

I hope continue with some exercises on the cycles probably tomorrow, though my internet connection has been acting up lately, so I am not sure.

Regarding the "30 days" simplification--I think I first ran across this on http://sengokudaimyo.com, but I'm pretty sure I've encountered it since then, but I'll have to find out where.

I should correct that, anyway, to saying that in the Heian period they appeared to have simplified the calendar-making, using extra months to often make up the difference so they would hit the appropriate solar dates when they were off. I do recall running into problems trying to put this into practice, however.

I need to find the specific calendar reforms. As I recall, it started off, in the Nara period, mimicking Chinese astronomy, but slacked off in the later Nara period, as the calendar side of the Onmyo-ryo was neglected in favor of the more mystical side of the equation; this split is often told via the tale of Abe Seimei and the son of his teacher, Kamo Yasunori. Seimei was given charge of the onmyodo side of the house, while the Kamo family remained in charge of the less prestigious duties of calendrical studies.

What always got me about the idea of the 30 days was that many banquets and festivals are for dates like "the first rat day" of X month. I'll try to find out more, however.

I can't recall any calendrical reforms prior to the Edo period, but during the Edo period I believe the calendar was reformed several times--you may have mentioned all of them, I'd have to check.

My source is a Rekishi Gunzou Special on the '3 Kingdoms' era of China that has a sidebar about the Chinese calendar. As with most Japanese books, it doesn't give a source but states that the 12 branches and 10 stems were thought to be of roughly the same age but that recent archeological finds indicate the branches are older. And of course, it doesn't give an indication of WHAT finds. A few paragraphs down it does state that the sexegenary cycle was already in use by the time the stem/branch cycles showed up-I missed that earlier.

I have worked mostly with the calendar "proper," that is, how do you name days; I don't know much about the divinatory use. Certainly, the onmyo-ryo was put in charge of making the calendar. Josh, maybe at some time you could prepare something on the divinatory calendar.

"using extra months to often make up the difference so they would hit the appropriate solar dates when they were off " The extra months are called intercalary months, and they are quite interesting. But they are not Heian period simplifications. They have been around at least since the 3rd mil. BC in Mesopotamia, and are in in the Shang bones as well. In China the rule for them was established by the 5th century BC, and this rule was used in Japan. At times Japan, at least, they sometimes changed which month was intercalary. What problems are you thinking of?

"What always got me about the idea of the 30 days was that many banquets and festivals are for dates like "the first rat day" of X month." In many cases it will help to think of the days of the 10- or 12-cycle as days of the week. "the second Tuesday of every month." "The first Sunday in April." You will have 2 or 3 days of each day of those cycles each month. Do they ever have "the second rat day" or the "third rat day"?
Anyway, here is a question:

Q5 What popular Japanese festival was originally celebrated on the first day of the snake of a certain month?

"I can't recall any calendrical reforms prior to the Edo period." That is right. The Senmyô calendar 宣明暦 was used from 862 AD to the Edo period.

Q6 Get familiar with the 10 and 12 cycles by writing the charters one by one o or at least as many as you have time for. Copy them one by one, or write using the kanji henkan of the kun-yomi. Of course, if you write them by hand, so much the better.

Q7 Identify the following by the number and by the kun-yomi. For numbers use 3-10 to mean the third element of the stem cycle, 8-12 to mean the 8th elecment of the branch cycle, and (10, 8 ), (10,8 ;20) or 20-60 for the 60-cycle.
丁、寅、庚、申、甲、午

Q8 Look at the ordered pairs of numbers of the 60-cycle. Do you see how it works? You determine each element separately based on the previous element. Of course, when you come to the end of the cycle, you start with 1.
Pick a random number between 1 and 60, find the ordered pair that corresponds with it, and write about 20 elements in the form (7,3;27). Afterwards see if you got it right.

Q9 Write the following cyclic numbers in the above format:
甲子 己亥 辛卯 戊未 丙辰) 癸亥. I suggest you memorize the first, at least.

Q10 The bone pictured above has the following:
癸酉卜 …五日丁丑
癸酉卜 …六日戊子
癸巳卜 甲午
Try to translate this using the number format for the cyclic days. Can you deduce anything about the divination practices of the time from this?

Q11 For mathematicians: what is the relationship between 10, 12, 60, and 120? What significance does that have for a certain answer above?

Okay, I might be missing some of the books I had read stuff in, but I think I have the basis for where the idea of the 30-day month came from, and I think it probably does trace back to the particular website in question:

"Each month had 30 days, and was nominally made up of three ten-day weeks. The last day in each week is taken to be a general day of rest. The first day of each month is called Tsuitachi, and the last day — a bigger deal of a “day off” than the tenth and twentieth — is called Misoka. The last day of the year is called Ô-Misoka (= Great Misoka)."

This was reinforced by Nakayama Shigeru's work: A History of Japanese Astronomy: Chinese Background and Western Impact, not because he claimed that it was 30 days, but for two other reasons:

1) On p. 10-11, Nakayama notes the decline of calendrical science in Japan: "But since the study of astronomy had been introduced as an integral part of the Chinese institutional framework, it deteriorated along with other aspects of Chinese culture in Japan. After about the tenth century the office of astronomer was hereditary, an inevitable development in view of the replacement of bureaucratic institutions by familistic ones. After the Hsuan-ming 宣明 calendar reform of 862, calendrical revision was neglected for a long period, despite the growing discrepancies between observed phenomena and the calendar in use."

2) Later on he makes the note that the Chinese emphasis was on astrology, calendar-making, time-keeping, and divination. The Japanese, on the other hand, seem to have ordered the value as "astrology and divination... followed by calendar-making and timekeeping." He then uses the story of Abe Seimei and Kamo Mitsuyoshi (son of Yasunori) as an example of the esteem the different branches were held in.

3) On p. 57, Nakayama specifically refers to the sexegenarian cycle as a "simplified" version of the calendar for the masses: "If astrologic calculations were to be draswtically simplified for widespread use in a culture where advanced mathematical training was not common, the replacement of an intricate system of celestial periods by a simple numerical cycle is hardly to be wondered at."

4) On p. 66, Nakayama lays out the adoption of calendar reforms between China and Japan, indicating that between 862 to 1685, there were no significant adoption of calendrical refroms in Japan (they continued to use the Xuanming (Hsuan-ming) calendar). This lack of interest in reform (at least one reform is mentioned, but it was never accepted) appears to stem from a lack of interest by Japan, as noted above.

I think I also absorbed some of the regularity of time presented by Bernard Frank in his work, Kata-imi et Kata-tagae:Étude sur les interdits de direction à l'époque Heian, and that would have further contributed to my idea that the months were regular.

I do find a counter to this in a note I had not previously read or had overlooked in The Pillow Book of Sei Shonagon, trans. by Ivan Morris, where he states: "Months... were either twenty-nine or thirty days long, with an intercalary month added about once every three years."

So my question: If they aren't correlated exactly, then how does one calculate the month v. the cycle? I realize that may be for later in the discussion.

Looks like we were posting at the same time. I'll see what I can draw up on the divinatory practices, but for now I'll try to get back to the current topics

Bethetsu wrote:

Q5 What popular Japanese festival was originally celebrated on the first day of the snake of a certain month?

It appears to be "Joshi no Sekku": The origins of the hina doll festival; in China it seems it was originally held on the 1st day of the snake in the 3rd month. It was difficult to find, which may be because it was quickly tied to the 3rd day of the month. Here we can turn to Sei Shonagon to see her description of it as "Momo no Sekku". I'm not sure when the changeover happened, however.

Q7 Identify the following by the number and by the kun-yomi. For numbers use 3-10 to mean the third element of the stem cycle, 8-12 to mean the 8th elecment of the branch cycle, and (10, 8 ), (10,8 ;20) or 20-60 for the 60-cycle.

Q8 Look at the ordered pairs of numbers of the 60-cycle. Do you see how it works? You determine each element separately based on the previous element. Of course, when you come to the end of the cycle, you start with 1.
Pick a random number between 1 and 60, find the ordered pair that corresponds with it, and write about 20 elements in the form (7,3;27). Afterwards see if you got it right.

You can always tell if you have a "bad" cycle indicator because the stem and branch will always agree regarding odd or even. To put it another way, the sum of two corresponding stem and branches will always be even.

Quote:

Q10 The bone pictured above has the following:
癸酉卜 …五日丁丑
癸酉卜 …六日戊子
癸巳卜 甲午
Try to translate this using the number format for the cyclic days. Can you deduce anything about the divination practices of the time from this?

I'm not currently seeing a pattern. It does appear that the sexegenary cycle is used for days, and the branch (decenary?) cycle is used for the year.

Out of curiosity, where did you get your sample? I'm looking through Collections of Oracular Inscriptions in France, by Jean A. Lefeuvre, and I'm not seeing anything quite like what you have. Also, I'm only seeing (癸酉) once; are you taking info from the picture, or does it come from the rest of the bone?

Quote:

Q11 For mathematicians: what is the relationship between 10, 12, 60, and 120? What significance does that have for a certain answer above?

Well, 10 x 12 = 120
But 10 x 12 / 2 = 60

I'm not sure how to express the idea of the sexegenary cycle in mathematical terms, but you end up with a repeat every 60 cycles. Just thinking out loud, each stem will appear 6 times and each branch will appear 5 times.

Let A = Stem (any number 1-10) and B = Branch (any number 1-12) such that the (A+B) mod 2 = 0. Therefore:

((6-(((B-A)/2+6) MOD 6)) mod 6) * 10 + A = Sexegenary cycle location.

That seems far too complicated, but appears to work. There has to be something simpler, I would think, but I'm not thinking very well at the moment, I guess. It may just prove that it is easier to have a chart :)

Not exactly sure if that's at all what you were looking for, but it was bugging me, earlier.

I did the exercises but didn't post them to avoid redundancy, since from a quick look they're all the same as Josh's (except for the 20 random pairs).

JLBadgley wrote:

You can always tell if you have a "bad" cycle indicator because the stem and branch will always agree regarding odd or even. To put it another way, the sum of two corresponding stem and branches will always be even.

Thanks for noting this-that's very handy.

JLBadgley wrote:

Also, I'm only seeing (癸酉) once; are you taking info from the picture, or does it come from the rest of the bone?

I think it's actually a typo and should be 癸未卜…六日戊子 (10,8,20)...6th day, (5,1,25).

I have to admit being confused as to where the characters 癸酉、癸未、癸巳 appear on the picture of the bone. I'm assuming that they appear on the bone using older symbols? So in the following pic, the three numbered boxes are the dates with the divination character at the end?

I'm also not sure where you arrived at the associated 'dates' for them (五日丁丑, 六日戊子, 甲午). Are these also on the bone using other symbols or were they arrived at using another method?

JLBadgley: Also, I'm only seeing (癸酉) once; are you taking info from the picture, or does it come from the rest of the bone?

I think it's actually a typo and should be 癸未卜…六日戊子 (10,8,20)...6th day, (5,1,25).

I have to admit being confused as to where the characters 癸酉、癸未、癸巳 appear on the picture of the bone. I'm assuming that they appear on the bone using older symbols? So in the following pic, the three numbered boxes are the dates?

I'm also not sure where you arrived at the associated 'dates' for them (五日丁丑, 六日戊子, 甲午). Are these also on the bone using other symbols or were they arrived at using another method?

Sorry, I was not clear and I made some mistakes like that typo and got the order wrong.
The photo is a detail from Shirakawa, Shizuka白川静, 1963, In Kôkotsu Bunshû殷・甲骨文集 [Collection of the Yin Oracle-bone Inscriptions] (Tokyo: Nigensha 二玄社). The transcriptions are from that book.

The writing is up to down. The order in which the oracles are transcribed (the order I give below) seems to be the order in which they were probably written. One bone could have several oracles on it.

The oracle on the left starts off 癸酉卜 and later on contains the phrase …五日丁丑
(the last two characters are at the top of the far left row)

I'm not sure if it is 5 days or "fifth day" in his context, but I would suspect that these are different divinations, with different questions, one divination every 10 days, so once a 'week', perhaps, with 3 divinations that month. I don't know that the other dates have much significance a they appear to be related to the outcome of the particular divinations, so without much more context I find it difficult to speculate.

Q5 What popular Japanese festival was originally celebrated on the first day of the snake of a certain month?
Josh:it appears to be "Joshi no Sekku": The origins of the hina doll festival; in China it seems it was originally held on the 1st day of the snake in the 3rd month. It was difficult to find, which may be because it was quickly tied to the 3rd day of the month. Here we can turn to Sei Shonagon to see her description of it as "Momo no Sekku". I'm not sure when the changeover happened, however.

Yes, it is Jôshi no sekku 上巳の節句. According to the J-Wiki, it was changed to 3.3 in the 魏 Wei (Gi) during the Three Kingdom Period.

Q7-9 You got them right, Josh. And you are right. Both the stem and branch have to be odd or have to be even.

Q10 At least as far as numbers go, the following works:
癸酉卜 …五日丁丑
I divine on day (10,10;1) [concerning something] on the fifth day [from today, the first day], that is on day (4,2;14). (There will be a ceremony related to the ancestor 中丁 that day)
癸未卜 …六日戊子
I divine on day (10,8;20) [concerning something] on the 6th day [from today, the first day], that is on day (5,1;25).
癸巳卜 甲午
I divine on day (10, 6;30) [concerning something tomorrow], that is on day (1,7;31).
The kanshi were not used for years for another millennium.

You are right that they normally divined every ten days (on a mizunoto day) about the next ten days. Those are not necessarily in the same month, however.

Q11 For mathematicians: what is the relationship between 10, 12, 60, and 120? What significance does that have for a certain answer above?

Josh, you got the point of the question.

In mathematical terms, 120 is the product of 10 and 12, and 60 is the "least common multiple". They are not the same because 10 and 12 have a factor in common, namely 2.
30 = (5 * {2) * 6}. That is why there are only odd or even pairs, i.e. (stem-branch) mod 2 = 0.
More generally, if you have for instance 12 and 30, the greatest common factor is 6, and you get a 60-cycle because (2 * {6) * 5} = 60. All a,b pairs must be in the relationship (a-b)mod 6 = 0. If the only common factor is 1, as 9 * 1 * 10, you get all 90 pairs.

Quote:

Let A = Stem (any number 1-10) and B = Branch (any number 1-12) such that the (A+B) mod 2 = 0. Therefore:

I tried it for one number, and it worked. I will take your word for it that it works in general.

Quote:

It may just prove that it is easier to have a chart

A chart is indeed easier than that.

Quote:

. There has to be something simpler, I would think,

Try this. Given a stem S and a branch B that have the relationship (S-B) mod 2 = 0, the position is {(S-B) mod 12 * 5} + S
For anyone not familiar with mod, here is a restatement:
For S and B both even or both odd,
if S>=B, (S-B)*5 + S,
if S<B, (12+S-B)*5 + S.

I still have some more to write about with Japanese dates, but I will not be able to prepare anything for a few days. If anyone would like to explain about the branches and stems in relation to the Chinese 5 elements (is that Han period?) this might be a good time to do it, if you have time now.

My understanding is that during the Han dynasty there was an attempt to bring just about every theory they could find together into a single and cohesive whole. This had been done, to a point, previously, but it almost seems as if the Chinese decided that all of the ancient masters had to be right, even if they seemingly contradicted each other.

Thus, you had the following numerologically significant theories:

The single whole.
The duality of yin and yang
The four directions and directional guardians
The five elements
The 8 trigrams
The 10 stems
The 12 branches
The 64 hexagrams
etc.

Obviously, everything divisible by two can fit in with the yin-yang theory, but the five elements are problematic. For those who don't know, the five elements are wood->fire->earth->metal->water->wood (given in the constructive cycle--so wood burns and creates fire, fire produces ash=earth, the earth creates metal, metal creates water (a stretch based on the way water droplets form on metal under certain conditions, perhaps?), and water feeds the growth of plants (wood). You can also reverse that same cycle and create a destructive cycle (fire destroys wood, etc.). However, there is a third cycle in here: fire->metal->wood->earth->water->fire. In this cycle, fire *weakens* metal, metal *weakens* wood, etc. This is where you get the classic star inside of a circle.

Well, in reconciling all of these, yin and yang were assumed to be the basic building blocks. Thus, each element must have different amounts of yin and yang inside, and you could therefore link each element to other things that also contain that balance of yin and yang--from animals, to land features, to internal organs. Finally, even to directions.

But there are four directions. So how do we reconcile this? Well, we add a fifth: The center. With that neatly taken care of we end up with the elements as follows:

You'll notice that the Center does not associate with one of the 12 stems, but it *does* associate with two of the 10 branches, since each branch is the elder or younger "brother" of a given element; I wonder when that particular association came about, as a matter of fact. Like the animals for the 12 stems, I wouldn't be surprised if it was either part of a later syncreticism or possibly just a mnemonic device.

BTW, each of the 8 directions is associated with a trigram, too. Now, since we have 12 stems and 8 trigrams, and we've already designated four of the directions, the rest get to share. In fact, you will find, as I think Tatsunoshi mentioned earlier, that people would actually use the 12 stems to designate one direction or another:

Bonus Question: Based on the above, what directions would the following stem combinations indicate?

丑寅
戌亥
辰巳
未申

Okay, it is late, and I don't guarantee that this makes much sense. I really need to pull out my sources when I do stuff like this, and frame it all much better, so I apologize if I've been somewhat rambling.

Bonus Question: Based on the above, what directions would the following stem combinations indicate?

丑寅-NE
戌亥-NW
辰巳-SE
未申-SW

Everything was quite clear, Josh. One question I have-by "having to share", I assume you mean that since there were 8 branches left and only four more directions each direction got two of the branches (like in the above)?

Right on both counts. There is basically one trigram for each of the 8 directions, so there are two branches for each of the four non-cardinal directions, which also were known as the four gates (天門、鬼門、地門、人門）.

As for the branch v. stem--I always get those mixed up. I usually think of them as the animals v. the elements

I just think it is amazing how they ended up fitting all of this together.

I don't really understand this. I have some questions, though I suspect that at least some are completely outside the concepts.

"Thus, each element must have different amounts of yin and yang inside": Does that mean, for instance that fire is 100% yang 陽 while earth is 25% yang and 75% yin 陰? Or is more involved than percentages? For the trigrams (unicode starting 2630), ☱,☲, and ☴ would all seem to have the same amounts of yin and yang (1:2), but I doubt they are all the same material.

How do the trigrams match directions?

I have never seen the branches used instead of "kita, " etc. in ordinary use, but I have seen the names for the corners, 丑寅 （艮), etc., used as pure directions.

My understanding is that you are essentially correct. Each, to borrow from Greek philosophy, platonic element would be 100%, 75%, or evenly balanced at 50% of each.

The trigrams don't always match up with the gogyo (wuxing; 五行) theory; probably another cludge that they had to deal with. Also, I believe configuration of yin and yang are just about as important as the quantities. To put it another way: Scrambled eggs, fried egg, and boiled egg all have the same amount of *stuff* (white and yolk), but the configuration is very different.

The trigrams get associated with the 8 directions mainly for geomantic purposes. It probably helps that they are associated with the yijing and divination, but I'll have to get back to my sources to get more info on it.

I've not seen the branches used for the cardinal directions, except, again, to illustrate some kind of geomantic principle. Again... I'll have to get to some of this after I return from Nepal.

Going back to cyclic days, they have not been used that much for dating days in Japan, but I will describe two uses.

One is for constructing calendars. Cyclic dates give a fixed grid that let you identify days in a year before you have determined months. (You can also compare two different calendars using them.)
In most calendar procedures, to construct the calendar for a certain year, first you determine the cyclic date and time of the winter solstice of the previous year, then the approximate (mean) cyclic date and time of the new moon previous to that. Based on those you calculate the cyclic dates and times of the solar terms (which we will discuss later) and of the true new moons.
Near the end of the process, you compare the cyclic dates of consecutive months. If the A of the dates are B, the first month is a long 30-day month (dai no tsuski 大の月), else it is short 29-day month (shô no tsuki 小の月）.

Q12 What words fit A and B in the above sentence?

Especially appropriate for the Ancient Japan Forum, perhaps,
The Nihon Shoki uses a highly roundabout way of expressing days of the month. Instead of saying, for instance, [670 AD] 夏四月三十日壬申 (summer, the 30th day (a mizunoue-saru day) of the fourth month) it uses 夏四月癸卯朔壬申 (the 壬申 (9,9;9) day in the 4th month, the first day 朔 of which is a 癸卯 (10,4;40) day). Since 癸卯 is the 40th day of the cycle and 壬申 is the 9th day of the cycle, one can calculated that the 壬申 day is the 30th day of the month.

Q 13 Give the numbers and ordinary date form for the dates below, as
夏四月癸卯朔壬申 (9,9;9) (10,4;40) 4月30日 (or 4.30).
The year date in brackets is not part of the original text.

I guess I was not clear. Probably I should have said the cyclic date of the new moon rather than the cyclic date of the month. OK, I will try it from the other direction.
If you have 九月乙巳朔 and the ninth month is a 30-day month, what will be the cyclic date of the first day of the 10th month? If it is a 29-day month, what will the cyclic date of the first day of the 10th month? What then is the (easy) relationship between the cyclic dates of the new moons and the length of the month?

Quote:

Q 14 What other Japanese texts do you know of that use the cycle for giving the days?